課程資訊

CALCULUS (GENERAL MATHEMATICS) (A)(1)

98-1

MATH1201

201 101A1

16

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/981calculusA16

1. 1.Functions and its properties(Exponential functions, inverse functions, and logarithms)

2.The tangent and velocity problems, the limit of a function, calculating limits using the limits laws, the precise definition of a limit

3.Continuity, limits at infinity; horizontal asymptotes

4.Derivatives and rates of change, the derivative as a function, derivatives of polynomials and exponential functions, the product and quotient rules

5.Derivatives of trigonometric functions, the chain rule, Implicit differentiation

6.Derivatives of logarithmic functions, rates of change in the natural and social science, related rates

7. Linear approximations and differentials, hyperbolic functions

8.Maximum and minimum values,the mean value theorem, how derivatives affect the shape of a graph

9.Indeterminate forms and L’Hospital’s rule, summary of curve sketching, Graphing with calculus

10.Optimization problems, Newton’s method, antiderivatives

11.Areas and distances, the definite integral, the fundamental theorem of calculus

12.Indefinite integrals and the net change theorem, the substitution rule

13.Areas between curves, Volumes, Volumes by cylindrical shells

14.Work, average value of a function, Integration by parts

15.Trigonometric integrals, trigonometric substitution

16.Integration of rational functions by partial fractions, strategy for integration, integration using tables

17.Approximate integration, improper integrals

To understand the fundamental skills and theory of finding the derivatives of functions and finding the integrations of functions

Office Hours

CALCULUS Early Transcendentals, by James Stewart, 6E, Thomson Books/Cole

CALCULUS Early Transcendentals, by James Stewart, 6E, Thomson Books/Cole

(僅供參考)

 No. 項目 百分比 說明 1. 期中考 50% 2. 期末考 50%

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